Individual skill

monte-carlo-methods

Monte Carlo simulation done well — sampling, variance reduction, MCMC diagnostics, and honest uncertainty quantification.

skills/monte-carlo-methods/SKILL.md

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## Overview

Monte Carlo methods solve integration, optimization, and inference
problems by random sampling — converging as 1/√N regardless of
dimension, which makes them the tool of last resort that usually works.
This skill covers direct sampling, variance-reduction techniques,
Markov chain Monte Carlo (Metropolis–Hastings, HMC/NUTS), and the
convergence diagnostics that separate real posteriors from random walks.

## When to use

- Estimating high-dimensional integrals or expectations
- Propagating uncertainty through a nonlinear model
- Bayesian inference: sampling posteriors with MCMC
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